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Prime means, or mean primes?


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#1 bonanova

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Posted 19 September 2007 - 08:39 AM

A prime, N, is a number with no factors other than [1,N].
Can the arithmetic mean of two consecutive prime numbers be itself a prime number?
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#2 cpotting

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Posted 19 September 2007 - 04:03 PM

A prime, N, is a number with no factors other than [1,N].
Can the arithmetic mean of two consecutive prime numbers be itself a prime number?


Perhaps I am misunderstanding your question, but it seems to me that you are asking if in
(p1 + p2)/2 =p3
can p3 be prime.

If that is right then the answer is NO. You stated that the two primes are consecutive. Since p3 would fall between p1 and p2, then p1 and p2 could not be consecutive primes since another prime exists between them.

Is that correct, or have I missed something?
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#3 bonanova

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Posted 19 September 2007 - 08:00 PM

That's it.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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